Today, mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences such as economics and psychology. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new disciplines. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered later.[7]

Fields of mathematics

As noted above, the major disciplines within mathematics first arose out of the need to do calculations in commerce, to understand the relationships between numbers, to measure land, and to predict astronomical events. These four needs can be roughly related to the broad subdivision of mathematics into the study of quantity, structure, space, and change (i.e., arithmetic, algebra, geometry, and analysis). In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.

Mathematical logic is concerned with setting mathematics on a rigid axiomatic framework, and studying the results of such a framework. As such, it is home to Gödel's second incompleteness theorem, perhaps the most widely celebrated result in logic, which (informally) implies that any formal system that contains basic arithmetic, if sound (meaning that all theorems that can be proven are true), is necessarily incomplete (meaning that there are true theorems which cannot be proved in that system). Gödel showed how to construct, whatever the given collection of number-theoretical axioms, a formal statement in the logic that is a true number-theoretical fact, but which does not follow from those axioms. Therefore no formal system is a true axiomatization of full number theory. Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoreticalcomputer science.

Discrete mathematics

Discrete mathematics is the common name for the fields of mathematics most generally useful in theoretical computer science. This includes computability theory, computational complexity theory, and information theory. Computability theory examines the limitations of various theoretical models of the computer, including the most powerful known model - the Turing machine. Complexity theory is the study of tractability by computer; some problems, although theoretically solvable by computer, are so expensive in terms of time or space that solving them is likely to remain practically unfeasible, even with rapid advance of computer hardware. Finally, information theory is concerned with the amount of data that can be stored on a given medium, and hence deals with concepts such as compression and entropy.

As a relatively new field, discrete mathematics has a number of fundamental open problems. The most famous of these is the "P=NP?" problem, one of the Millennium Prize Problems.[20]

Applied mathematics

Applied mathematics considers the use of abstract mathematical tools in solving concrete problems in the sciences, business, and other areas. An important field in applied mathematics is statistics, which uses probability theory as a tool and allows the description, analysis, and prediction of phenomena where chance plays a role. Most experiments, surveys and observational studies require the informed use of statistics. (Many statisticians, however, do not consider themselves to be mathematicians, but rather part of an allied group.) Numerical analysis investigates computational methods for efficiently solving a broad range of mathematical problems that are typically too large for human numerical capacity; it includes the study of rounding errors or other sources of error in computation.

Kami terinspirasi

A Vast and most Excellent Science
How often at night
When the heavens were bright
with the light of the glittering Star and Moon
have I stood there amazed and asked as I gazed
if their glory exceeds that of ours.
-Anonymous&H2O-

Anyone who has never made a mistake has never tried anything new.-Albert Einstein-

The Atom and the Quantum
Hail to Max Planck, Einstein, Bohr, Pauli, Broglie, Schrödinger, Feynman,
and Young man in the Future from the worshipful! You are the Master by
whom we are led. Awed by your cryptic and proud affirmations. Each of us,
driven half out of their head, still remains true to you
wouldn't say boo to you, Swallows your theories from Alpha to Zed,
Even if (drink to him, tankards must clink to him!) None of us fathoms
a word you have said
-George G.& H2O-

Particles and Waves
We are trapped by language to such
a degree that every attempt to formulate
insight is a play on words.
(2πrmv = n h)
n = 2πr/λ
n = an integral number
λ = wave length
h = Planck's Constant
2πr = Circle's Constant (Orbit equation)
-Niels Bohr& -H2O-

Does God Play Dice?

But you tell me of an invisible planetary system
where electrons gravitate around a nucleus. You explain
this to me with an image, I realize then that you have been
reduced to poetry:
" I shall never know. I have the time to become indignant?
you have changed theories. so that the sciences that was
to teach me everything ends up in a hypothesis,
that lucidity founders in metaphor, that uncertainty
is resolved in a work of art

-A.Camus, The Myth of Sisyphus.-

Schrödinger's Cat
The law of chaos is the law
of ideas, of improvisations
and seasons of belief

The Dreams stuff is made of

Like a gleam in the darkness, we have appeared
for an instant from the black nothingness of the
ever-unconscious matter, in order to make good
the demands of reason and create a life worthy
of ourselves and of the Goal we only dimly perceive
-Andrei Sakharov-

Quantum field Theories
"The nature of a field is completely determined by
the properties of the particle that transmit it,
while the nature of a particle depends solely on
the ways in, which it couples to fields.
QED = Quantum Electrodynamic
α = e2/ħc
QCD = Quantum Color Dynamic (Quantum Foam)
rp = Second root of Għ/c3 = 1,6 x 10-35(power) it is Planck's Length
-Richard Feynman,Julian Schwinger, Murray Gell-mann and George zweig
&
-H2O-

The whole Shebang
I am astounded by people who want
to "know" the universe when it's hard
enough to find your way around the world
-H2O-